Soak wooden skewers in water and allow to soak for at least 30 minutes before grilling so they do not burn on the grill.
Pat the shrimp dry, then season with salt and pepper on all sides.
In a large bowl, whisk together all of the marinade ingredients: the olive oil, lemon juice, lemon zest, garlic, most of the parsley (save 1 Tablespoon for garnish), oregano, and paprika.
Add shrimp to the bowl and lightly toss to coat the shrimp with the marinade.
Cover and refrigerate for 15-20 minutes, maximum. Don't marinate for longer than 20 minutes, or the shrimp may start cooking because of the acidity of the lemon.
Thread the shrimp onto skewers. I find 4-5 shrimp per skewer is a nice amount.
Grill over medium-high heat for 2-3 minutes each side.